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Innovation in the States: A Diffusion Study*

Published online by Cambridge University Press:  01 August 2014

Virginia Gray*
Affiliation:
University of Minnesota

Abstract

This study focuses on a nonmonetary dimension of public policy—innovation by states in the fields of education, welfare, and civil rights. Innovation is considered equivalent to the adoption of a law by a state. From the literature on diffusion (or spread) of innovations, the explanation of user interaction is taken, and a simple model with an interaction term is constructed. The model performs fairly well when evaluated by several common criteria. The results do vary somewhat from one issue area to another; other types of supplementary analysis also indicate variation in diffusion patterns according to the issue involved. Political and economic differences among states are found to account for differences in time of adoption, and “innovativeness” is shown to be an issue- and time-specific factor.

Type
Research Article
Copyright
Copyright © American Political Science Association 1973

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Footnotes

*

The author wishes to acknowledge with gratitude the constructive criticisms of Professor John Sprague and Professor James W. Davis, Jr., Washington University, and Professor John Wanat, University of Kentucky. The author is also grateful for the financial support of the Woodrow Wilson Foundation.

References

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2 Rogers, Everett M., Diffusion of Innovations (New York: Free Press of Glencoe, 1962), p. 13 Google ScholarPubMed.

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21 More elaborate models could be constructed in which there is diffusion from a constant source like the federal government, or in which there is incomplete mixing of the population, e.g., regional or professional communication networks may produce distinctive diffusion patterns. For these more elaborate models see: Coleman, James S., Introduction to Mathematical Sociology (New York: Free Press of Glencoe, 1964), chap. 17Google Scholar.

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25 It should also be noted that several sources of error are possible in this model. First of all, the data are recorded as proportions based on 48 states; obviously, there were less than 48 states in existence for many years studied. Nevertheless, the model fits best for the longer processes (i.e., education) in which more states are absent; hence, this possible source of error did not have deleterious effect on the goodness of fit.

Another kind of error could arise from using a lagged dependent variable on the right-hand side of the regression equation; the assumption that the stochastic or disturbance term is normally and independently distributed may be violated in such a situation. A common test statistic for the presence of serial correlation (i.e., the disturbance at t is highly correlated with the disturbance at t-1) is the Durbin-Watson d. When proper adjustments are made for using a lagged dependent variable, the d-test indicates no serial correlation. (See Christ, Carl F., Econometric Models and Methods [New York: John Wiley & Sons, 1966], p. 522)Google Scholar. Another test for normality is to collect the residuals into a frequency distribution and graph them. (See Christ, pp. 526–530). If the residuals are approximately normal, the graph will be bell-shaped. When this test was applied to three of the laws, the residuals did not appear by inspection to be normally distributed. Thus, the results of the two tests are conflicting concerning the error terms.

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29 For more complete explanation of these measures and their data sources, see Gray, chap. 2.

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